Hydrogen has been considered as an alternative source of fuel to the fossil fuel in future, most especially, for mobile applications. However, a requirement is the safe, efficient and compact on- board storage of hydrogen. Reversible storage in metal hydride is promising, but adequate knowledge of materials system fulfills all requirements regarding hydrogen content is a major drawback, release temperature, and reversibility simultaneously. Hydrogen absorption- desorption in a metal hydride bed reactor can be modeled using different software such as FLUENT, CFD-ACE, and COMSOL Multiphysics. This book chapter will focus on the use of software COMSOL Multiphysics to simulate the diffusion and heating of hydrogen and metal hydride powder in both radial and axial directions. The model consists of system of partial differential equations (PDE) describing two-dimensional heat and mass transfer of hydrogen in a porous matrix. The influence of the operating parameters Temperature, Pressure, Concentration, Permeability and Thermal Conductivity on the rate of absorption-desorption of hydrogen in metal hydride will be fully discussed. The simulation results obtained could be applied to the on - board hydrogen storage technology, in particular for the hydrogen supply of a fuel cell for powering of a hydrogen fuel cell vehicle.